We investigate the performance of a network system on the World-Wide Web employing proxies that interact with a pool of servers to service a pool of client requests. We focus on modelling the interaction of a proxy with the server system and its performance in maximizing the number of requests that can be served. We formulate the problem using a discrete time Markov chain model capturing the state of the client (equivalently the state of the proxy) and quantify the performance in terms of number of requests that are successfully processed by the server system. We derive a closed-form solution to determine the percentage of requests that can be admitted by the servers, referred to as admission control factor, which is our performance metric of interest. We conduct a systematic and rigorous simulation study to demonstrate the behavior of our performance metric with respect to the number of client requests and the number of available servers in the system. We also study the effect of server response time and propose three different strategies that a proxy may adopt to tune the performance of the system. The behavior of the three strategies - Conservative, Greedy, and Incremental Tuning, with respect to our performance metric is rigorously studied under a variety of system dependent parameters, with respect to the probability of a client request, and the probability of a new request arrival. Further, we perform an asymptotic analysis to quantify the ultimate performance limits of the admission control factor with respect to the number of client requests than can be supported by the system and the number of servers in the system. In the study with respect to the number of servers, we derive an exact bound on the behavior of our performance metric and testify this finding with our rigorous simulation experiments. Several interesting features are highlighted and the model is conclusively shown to be robust and elegant in capturing the behavior of the system.